Why is the height of the rail cushion nose not at the center of the ball?
Here is the rail cushion nose height specification, as dictated by the WPA:
Rail height (nose-line to table-bed) should be 63 ½% (+1 %) or between 62 ½% and 64 ½ % of the diameter of the ball.
If the cushion nose height were at the ball center (0.5D), instead, rebounding balls would slide more and would hop significantly if they come into the cushion with topspin (especially at fast speed).
Another obvious height would be at the “center of percussion” of the ball (0.7D), per TP 4.2, so the rebounding balls would tend to roll away from the rails more naturally. However, this height would tend to drive a rebounding ball down into the table, which would tend to slow the ball more, accelerate cloth wear (and faster formation of a “rail groove”), and cause the rebounding ball to hop.
The WPA 0.635D offers a good compromise between the 0.5D and 0.7D values. This height was determined empirically to result in good rebound performance without too much ball hop or cloth wear.
If the cushion nose height is a little higher than spec, balls will usually rebound a little slower and bank longer; and if the cushion nose height is a little lower than spec, balls will usually rebound a little faster and bank shorter. Everything can also vary some with cushion and cloth conditions. Balls will usually bank longer with new and slick cloth.